Question: Given $ m \angle AOB = 3x + 4$, $ m \angle BOC = 8x - 28$, and $ m \angle AOC = 108$, find $m\angle AOB$. $O$ $A$ $C$ $B$
Answer: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {3x + 4} + {8x - 28} = {108}$ Combine like terms: $ 11x - 24 = 108$ Add $24$ to both sides: $ 11x = 132$ Divide both sides by $11$ to find $x$ $ x = 12$ Substitute $12$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 3({12}) + 4$ Simplify: $ {m\angle AOB = 36 + 4}$ So ${m\angle AOB = 40}$.